Question

When Keisha installed a fence along the 200-foot perimeter of her rectangular back yard, she left an opening for a gate. In the diagram below, she used x to represent the length, in feet, of the gate. What is the value of x?

Answer 1

10

Explanation:

2(x + 60) + 2(30) = 200

2x + 120 + 60 = 200

2x + 180 = 200

2x = 20

x = 10 ft

Answer 2

Hello!

The answer is:

The value of "x" is 10 feet.

Why?

To find the correct answer to this problem, we need to remember the formula to calculate the perimeteer of a rectangle, it's given by the following equation:

`Perimeter=2length+2width`

Now, we are given that:

`Perimeter=200feet\\Width=30\\Length=x+60`

Then, substituting into the equation, we have:

`200feet=2(x+60feet)+2*(30feet)`

Applying the distributive property, we have:

`200feet=2x+120feet+60feet`

`200feet-120feet-600feet=2x`

`2x=200feet-120feet-60feet\\\\x=(20feet)/(2)=10feet`

Hence, the length of the gate is 10feet.

Have a nice day!